Exponential Growth Questions
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1 Researchers find that there are 60 raccoons on an island. When they return a year later, they find that there are 84. Assuming an exponential growth pattern, what is the annual population growth rate for the raccoons?
2 Your friend sends out a change letter e-mail to 12 people by the next day 15 people have received the letter. Assuming an exponential growth pattern, what is the daily growth rate for the number of chain letters received?
3 An arborist creates a table of different tree height patterns over a 4 year period. Which of the
trees has an exponential growth pattern? Why?
a. Complete the table by computing the absolute and relative change.
b. Which model would better represent this data, linear or exponential. Write a meaningful sentence to explain your answer.
c. Find the model for this data.
d. What value does your model predict when time is 8?
5 Consider the data in the table.
a. Complete the table by computing the absolute and relative change.
b. Which model would better represent this data linear or exponential? Write a meaningful sentence to explain your answer.
c. Find the model for this data.
d. What value does your model predict when time is 8?
6 According to the 2010 United States Census, the population of Lafayette was 67,140, roughly a 19% increase from 56,397 in 2000.
Construct an exponential model for Lafayette's population.b. User your model to predict Lafayette's population in 2020.
7 Frogs—A species of frog's population grows 24% every year. Suppose 100 frogs are released into a pond.
Construct an exponential model for this population.
How many frogs will there be in 5 years?
How many frogs will there be in 10 years?
About when will there be 1000 frogs?
8 Pandas—There is a well-studied Panda population in Wuyipeng. In 1981 there were 25 pandas and the researchers determined that they had an annual population growth of 1.066.
www. bearbiology.com
Construct an exponential model for this population.
Assuming no deaths, how many pandas would the researchers expect by 2001?
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Solution Summary
Step by step solutions are given. The Excel file contains formulas, computations and solutions used for the tables.
Solution Preview
1
84/60 - 1 = 0.4
Convert to a percent.
0.4 * 100% = 40%
2
15/12 - 1 = 0.25
Convert to a percent.
0.25 * 100% = 25%
3
Find the relative change for each tree's height pattern. The willow tree has an exponential growth pattern because relative change for the willow is constant.
Relative change
Time
Yew
Willow
Mulberry
Yew
Willow
Mulberry
0
2
4
2
NA
NA
NA
1
3.5
6
4
75%
50%
100%
2
5
9
6
43%
50%
50%
3
6.5
13.5
10
30%
50%
67%
4a
Time
Value
Absolute ...
Education
- MSc, California State Polytechnic University, Pomona
- MBA, University of California, Riverside
- BSc, California State Polytechnic University, Pomona
- BSc, California State Polytechnic University, Pomona
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